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Answer: The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.
Step-by-step explanation: Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.
We are to find the price per pound of apples and bananas.
The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.
Then, according to the given information, the system of equations describing the situation is as follows:
Multiplying equation (i) by 2, we have
and multiplying equation (ii) by 3, we have
To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at
From equation (i), we get
Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.